Averaging over Heegner Points in the Hyperbolic Circle Problem
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Averaging over Heegner Points in the Hyperbolic Circle Problem. / Petridis, Yiannis N.; Risager, Morten S.
I: International Mathematics Research Notices, Bind 2018, Nr. 16, 2018, s. 4942-4968.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Averaging over Heegner Points in the Hyperbolic Circle Problem
AU - Petridis, Yiannis N.
AU - Risager, Morten S.
PY - 2018
Y1 - 2018
N2 - For Gamma = PSL2(Z) the hyperbolic circle problem aims to estimate the number of elements of the orbit Gamma z inside the hyperbolic disc centred at z with radius cosh(-1) (X/2). We show that, by averaging over Heegner points z of discriminant D, Selberg's error term estimate can be improved, if D is large enough. The proof uses bounds on spectral exponential sums, and results towards the sup-norm conjecture of eigenfunctions, and the Lindelof conjecture for twists of the L-functions attached to Maass cusp forms.
AB - For Gamma = PSL2(Z) the hyperbolic circle problem aims to estimate the number of elements of the orbit Gamma z inside the hyperbolic disc centred at z with radius cosh(-1) (X/2). We show that, by averaging over Heegner points z of discriminant D, Selberg's error term estimate can be improved, if D is large enough. The proof uses bounds on spectral exponential sums, and results towards the sup-norm conjecture of eigenfunctions, and the Lindelof conjecture for twists of the L-functions attached to Maass cusp forms.
U2 - 10.1093/imrn/rnx026
DO - 10.1093/imrn/rnx026
M3 - Journal article
VL - 2018
SP - 4942
EP - 4968
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 16
ER -
ID: 209574604